Let point R be on the X-axis which is equidistant from points P and Q.
Point R lies on X-axis.
∴ its y co-ordinate is 0.
Let R = (x, 0) R is equidistant from points P and Q.
∴ PR = QR
= \(\sqrt {(x - 2)^2 + [0 - (-5)]^2}\) ....[By distance formula]
= \(\sqrt {[x- (-2)]^2 + (0 - 9)^2}\)
∴ (x – 2)2 + [0 – (-5)]2 = [x – (- 2)]2 + (0 – 9)2 …[Squaring both sides]
∴ (x – 2)2 + (5)2 = (x + 2)2 + (-9)2
∴ 4 – 4x + x2 + 25 = 4 + 4x + x2 + 81
∴ – 8x = 56
∴ x = -7
∴ The point on X-axis which is equidistant form points P and Q is (-7, 0).
